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A symmetry-extended Maxwell treatment of the net mobility of periodicbar-and-joint frameworks is used to derive a sufficient condition for auxeticbehaviour of a 2D material. The type of auxetic behaviour that can be detectedby symmetry has Poisson's ratio -1, with equal expansion/contraction in alldirections, and is here termed equiauxetic. A framework may have asymmetry-detectable equiauxetic mechanism if it belongs to a plane group thatincludes rotational axes of order n = 6, 4, or 3. If the reduciblerepresentation for the net mobility contains mechanisms that preserve fullrotational symmetry (A modes), these are equiauxetic. In addition, for n = 6,mechanisms that halve rotational symmetry (B modes) are also equiauxetic.

Symmetry detection of auxetic behaviour in 2D frameworks